This invention relates to improved methods for the formation of periodic structures of dielectric material, particularly photonic band gap materials, and to the structures formed by the improved methods.
Photonic crystals or photonic band gap materials comprise crystal-like structures in which the dielectric constant varies periodically in space. The behavior of electromagnetic waves in photonic crystals may be analogized to that of electron waves in natural crystals. Analogous to a band gap in a semiconductor, if the contrast in dielectric constant is large enough in a photonic crystal, a xe2x80x9cfrequency gapxe2x80x9d or xe2x80x9cphotonic band gap,xe2x80x9d may result, in which electromagnetic waves within the frequency gap are forbidden, irrespective of propagation direction. In other words, light or other electromagnetic radiation within the frequency gap cannot propagate, in any direction, within the crystal. Within the crystal, emission of photons at frequencies within the gap is thus prevented.
The potential for strict control of emission and propagation of light provides many potential applications in wide-ranging fields.
For example, since the decay rate of an excited atom or molecule is proportional to the density of photon states available for the transition, the frequency gap can be used to severely modify the lifetimes of excited chemical species situated within the photonic crystal. Immersing an excited atom or molecule in a photonic band gap material can increase or decrease the density of photon states available for the transition, thus enhancing or suppressing the decay rate of the excited species. Such selective modification of excited species lifetime will be very useful in photocatalytic processes to increase yield and/or selectivity of desired reactions.
Other applications envisioned for suppression of spontaneous emission by photonic crystals include: (1) use in lasers (particularly semiconductor lasers) to increase efficiency or to control or limit modes; (2) use in forming single-mode LEDs (3) use in solar cells to increase efficiency; (4) use in optical communications to increase available bandwidth and (5) use in quantum-optical devices. Still other applications that have been foreseen include chromatography, host-guest systems, thermal and/or electric shields or insulators, porous electrodes or electrolytes, waveguides, antenna substrates or shields, optical filters and reflectors, and paint pigments. Applications to optical switching and optical computing may also be found.
While the potential applications for photonic crystals are many, they are difficult to make. Present fabrication methods are generally time consuming and expensive, not likely to accommodate commercial production, and not generally amenable to application on curved surfaces. Present methods include (1) use of microlithographic techniques for assembly of a periodic semiconductor structure and (2) use of a self-ordering colloidal suspension of monodisperse silica or polystyrene spheres to form a close-packed template for forming an ordered dielectric matrix.
Method (1), microlithographic fabrication, is relatively uneconomical, particularly for larger crystals.
Method (2), use of monodisperse spheres to form a close-packed template of such spheres, is economically attractive because monodisperse colloidal suspensions of silica or polystyrene can self-assemble into close-packed structures at optical length scales, with excellent long-range periodicity. But creation of photonic gaps utilizing such close-packed structures requires interconnected lower-index spheres in an interconnected dielectric background of higher index. Optimum photonic effects require a low filling ratio (20-30%) of the dielectric background. Thus the template structurexe2x80x94with lower-index material surrounding higher-index spheresxe2x80x94must be used to form a structure with the relative indices reversed in order to achieve the desired photonic crystal structure. Difficulty has arisen in achieving such reversal. While dielectric materials with periodic pores have been fabricated using sol-gel techniques to form a dielectric matrix around the spheres of the template, followed by removal of the spheres, such fabrication is difficult and time-consuming, and definitive evidence of a photonic band gap has not been detected in the resulting structures.
The present invention provides an efficient, reliable method for the formation of photonic crystals. Materials produced by the inventive methods have shown definitive evidence of a photonic band gap.
According to the present invention, rather than forming a close-packed template of microspheres then substituting a dielectric for the material in the spaces, an aqueous sol is formed of a ceramic material, such as a nano-crystalline dielectric particles, and monodisperse microspheres such as polymer spheres. The dielectric material is thus incorporated during formation of the close-packed structure. A semiconductor material may be substituted for the dielectric material, if desired.
The desired quantity of the dielectric material (in terms of volume fraction of solids) is calculated from the expected geometric structure such that it just fills the voids between the microspheres at a packing efficiency, for the dielectric particles, of approximately 50-60%, with allowance for shrinkage in both drying and firing. For the typical fcc (face-centered cubic) structure, the desired quantity of dielectric particulate material is about 26% of the total solids volume.
Excess particulate material will result in a spreading of the polymer spheres and an increase in the filling ratio. Excess polymer spheres will result in incomplete matrix development and possibly higher friability of the finished structure. The amount of water can be adjusted to change the viscosity of the sol and thereby affect the dynamics of the self-ordering process.
Surface modifying agents (e.g. deflocculants, dispersants) can be used to improve the dispersion characteristics of the sol and the ordering behavior thereof by minimizing agglomeration and settling of the dielectric or semiconductor particulates. The pH of the suspension can be altered to change the surface charge of both the particles and the polymer spheres, again affecting the ordering behavior.
As microspheres, polystyrene, carboxylate-modified polystyrene and styrene/divinylbenezene (SDVB), available from Seradyn, 1200 Madison Ave, Indianapolis, Ind., 46225, have been used by the inventors hereof. Any polymer that can be manufactured as a sphere with the appropriate size and size distribution characteristics and which is amenable to removal by pyrolysis or by chemical methods could potentially be used. For a photonic band gap at optical frequencies, sphere diameters should be between 200 nm and 2 xcexcm, depending on the desired position of the band gap and the processing shrinkage. Uniform packing requires that the sphere diameters vary by less than 1%.
Any of a number of dielectric or semiconducting materials can be employed, provided that the dielectric or semiconducting material can be made with a sufficiently small particle size (from 10-80 nm depending upon the polymer sphere size used) such that thousands of particles can fit in a single void between polymer spheres. Also, it must be possible to disperse the particles. Example particulate dielectric or semiconductor materials include TiO2, Al2O3, SiO2, ZrO2, and MTiO3 where M is one or more rare earth metal ions.
The sol is deposited on a substrate and allowed to dry slowly, under controlled humidity conditions. The sample may be pressed in a cold isostatic press to increase the as-dried density and reduce stress cracks appearing during subsequent heat treatment. The sample is then calcined to burn off the polymer spheres, leaving air spheres in a dielectric or semiconductor matrix. Thin films with dimensions of about 10 mm by 2-3 mm can be reproducibly synthesized in about one day, in much shorter time than with previously known colloidal suspension techniques. The films have highly ordered domains extending from about 50-100 xcexcm, exhibiting better short-range and long-range order than previous macroporous materials fabricated from colloidal suspensions.
The substrate may be glass (for ease of characterization of the film) or any substrate that can withstand the required processing temperatures, can be compatible with the thermal expansion of the dielectric solid, and is smooth enough for an even film deposition.
The drying step is preferably performed for a time in the range of about 10 hrs to about 40 hrs, desirably for about 24 hours, at a humidity in the range of about 70% to about 99%, desirably about 95%, and at a temperature in the range of about 60xc2x0 F. to about 150xc2x0 F., desirably about 76xc2x0 F.
The pressing step is desirably performed by placing the sample, in a evacuated, sealed, latex bag, in an incompressible pressure-transmitting oil, then ramping up in 5 minutes to between 100-200 MPa, desirably, 170 MPa, holding for 2 minutes, then releasing pressure.
The calcination step is designed according to the components of the system. If the system includes a polymer steric repulsion agent (dispersant), then the heating rate must be slowed at the appropriate temperatures to allow for complete removal of that polymer, as well as the polymer spheres.
The calcination step desirably includes slowly heating the sample, at a rate of about 70-80xc2x0 C./hr, to a calcination temperature in the range of about 500 to about 900, desirably about 520xc2x0 C. The calcination temperature is then maintained for a time in the range of about 2 to about 10 hours, followed by cooling to room temperature at a rate of about 70-80xc2x0 /C./hr.
Further features, objects, and advantages of the invention will be apparent from the detailed description which proceeds below with reference to the following figures: